Series- summary 2025, Lecture notes of Fourier Transform and Series

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PURE 4.6 Series sequence = an ordered set of numbers eg: Oy, a, - 2 Oy 4,4 Finite infinite > Rest term / continues forever at ¥ index + lost term LO n 4 4.Ginomial expansion of (a + b) eg db \. _~ ( ‘tuo terms —— coefficient ne 4 (ato) = Hl AAAA (aby = la + 1h . 7 wok kook (ath) = la? +2ab +10? & Osea: (aby = a? +Gu2b +Gub? +8", ty M all terms have o (ai y= lat + 4a + 606? + 4ab? — 164 YO sotol arden of @ > coefficients form a pattern. “Pascal triangle” D \ 41 Method 4. The next row is then: z15 WS 1 9 Sa'b + IWa'b’ + IDab’ + 5ab%+4b° + Method 2, 7 1 m in | r 1 anchon on eaenlater (ME HS —_ \ stats. 5.9. Combinations / = position * (1) * oh eg (asb)”. Find coefRcient for (9 +4) tem Ss etatitr (8) ott ja° + Sab + (l0a°b® + IDa'b” + Sab! + 4b {5\ (>) [5\ FP \ “tom (o] UG) Ly coetficient = 5 (s] always star's — __+ at 0 2. Binomial coefficients = coefficients in expansion of (4#x)" bigger numbers ~~ better way #0 deal with Cn is a positive integer ) ot) “(s)e (ee + (“Je 5 where (44) term = ( nt r o\e - ; (r\ Be, where, (rt) term, -(*) n arr a ob 3. Arithmetic term progressions = linear sequence + + + a nd 4 e By 3 4 +d 4d as an aa 4 4 + 1 “ ard atad | ———__ n™ terms as ln-4)d 4 ( first terme 10 it ah 5 +3 —— > a@t3d arid common difference. L+ last term